## ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test

These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test.

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**Question 1.**

**Find the remainder when 2x ^{3} – 3x^{2} + 4x + 7 is divided by**

**(i) x – 2**

**(ii) x + 3**

**(iii) 2x + 1**

**Solution:**

f(x) = 2x

^{3}– 3x

^{2}+ 4x + 7

(i) Let x – 2 = 0, then x = 2

Substituting value of x in f(x)

f(2) = 2 (2)

^{3}– 3 (2)

^{2}+ 4 (2) + 7

= 2 × 8 – 3 × 4 + 4 × 2 + 7

= 16 – 12 + 8 + 7 = 19

Remainder = 19 Ans.

(ii) Let x + 3 = 0, then x = – 3

Substituting the value of x in f(x)

**Question 2.**

**When 2x ^{3} – 9x^{2} + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.**

**Solution:**

Let x + 1 = 0 then x = – 1,

Substituting the value of x in f(x)

f(x) = 2x

^{3}– 9x

^{2}+ 10x – p

**Question 3.**

**If (2x – 3) is a factor of 6x ^{2} + x + a, find the value of a. With this value of a, factorise the given expression.**

**Solution:**

Let 2 x – 3 = 0 then 2x = 3

=>x = \(\\ \frac { 3 }{ 2 } \)

Substituting the value of x in f(x)

**Question 4.**

**When 3x ^{2} – 5x + p is divided by (x – 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x^{2} – 5x + p – 3.**

**Solution:**

f(x) = 3x

^{2}– 5x+ p

Let (x – 2) = 0, then x = 2

f(2) = 3 (2)

^{2}– 5(2) + p

= 3 x 4 – 10 + p

= 12 – 10 + p

= 2 + p

**Question 5.**

**Prove that (5x + 4) is a factor of 5x ^{3} + 4x^{2} – 5x – 4. Hence factorise the given polynomial completely.**

**Solution:**

f(x) = 5x

^{3}+ 4x

^{2}– 5x – 4

Let 5x + 4 = 0, then 5x = – 4

=> x = \(\\ \frac { -4 }{ 2 } \)

**Question 6.**

**Use factor theorem to factorise the following polynomials completely:**

**(i) 4x ^{3} + 4x^{2} – 9x – 9**

**(ii) x**

^{3}– 19x – 30**Solution:**

(i) f(x) = 4x

^{3}+ 4x

^{2}– 9x – 9

Let x = – 1,then

f( – 1) = 4 ( – 1)

^{3}+ 4 ( – 1)

^{2}– 9 ( – 1) – 9

**Question 7.**

**If x ^{3} – 2x^{2} + px + q has a factor (x + 2) and leaves a remainder 9, when divided by (x + 1), find the values of p and q. With these values of p and q, factorise the given polynomial completely.**

**Solution:**

f(x) = x

^{3}– 2x

^{2}+ px + q

(x + 2) is a factor

f( – 2) = ( – 2)

^{3}– 2( – 2)

^{2}+ p ( – 2) + q

**Question 8.**

**If (x + 3) and (x – 4) are factors of x ^{3} + ax^{2} – bx + 24, find the values of a and b: With these values of a and b, factorise the given expression.**

**Solution:**

f(x) = x

^{3}+ ax

^{2}– bx + 24

Let x + 3 = 0, then x = – 3

Substituting the value of x in f(x)

**Question 9.**

**If 2x ^{3} + ax^{2} – 11x + b leaves remainder 0 and 42 when divided by (x – 2) and (x – 3) respectively, find the values of a and b. With these values of a and b, factorise the given expression.**

**Solution:**

f(x) = 2x

^{3}+ ax

^{2}– 11 x + b

Let x – 2 = 0, then x = 2,

Substituting the vaue of x in f(x)

**Question 10.**

**If (2x + 1) is a factor of both the expressions 2x ^{2} – 5x + p and 2x^{2} + 5x + q, find the value of p and q. Hence find the other factors of both the polynomials.**

**Solution:**

Let 2x + 1 = 0, then 2x = – 1

x = \(– \frac { 1 }{ 2 } \)

Substituting the value of x in

**Question 11.**

**When a polynomial f(x) is divided by (x – 1), the remainder is 5 and when it is,, divided by (x – 2), the remainder is 7. Find – the remainder when it is divided by (x – 1) (x – 2).**

**Solution:**

When f(x) is divided by (x – 1),

Remainder = 5

Let r – 1 = 0 => x = 1

Hope given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test are helpful to complete your math homework.

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